Windows into Elementary Mathematics:Alternate public images of mathematics and mathematicians

Research on students’ (and teachers’) images of mathematics and mathematicians reveals a number of stereotypical images, most of which are negative. In this paper we present an overview of some these images and stereotypes and consider the questions: (1) how might the image of mathematics and mathematicians be a problem in mathematics education, and (2) what can be done to remedy the situation? Also, we consider an outreach project called Windows into Elementary Mathematics. In this project mathematicians are interviewed about their perspectives on elementary mathematics topics and their interviews are videotaped and are posted online, along with supporting images and interactive content. In this context we consider the questions: (3) what is the Windows project about, and (4) how might it offer an alternate (and perhaps better) image of mathematics and mathematicians? Lastly, we share an example where activities from the project were used in a math-for-teachers course.

Voice disorders in teachers: clinical, videolaryngoscopical, and vocal aspects

Dysphonia is more prevalent in teachers than among the general population. The objective of this study was to analyze clinical, vocal, and videolaryngoscopical aspects in dysphonic teachers. Ninety dysphonic teachers were inquired about their voice, comorbidities, and work conditions. They underwent vocal auditory-perceptual evaluation (maximum phonation time and GRBASI scale), acoustic voice analysis, and videolaryngoscopy. The results were compared with a control group consisting of 90 dysphonic nonteachers, of similar gender and ages, and with professional activities excluding teaching and singing. In both groups, there were 85 women and five men (age range 31-50 years). In the controls, the majority of subjects worked in domestic activities, whereas the majority of teachers worked in primary (42.8%) and secondary school (37.7%). Teachers and controls reported, respectively: vocal abuse (76.7%; 37.8%), weekly hours of work between 21 and 40 years (72.2%; 80%), under 10 years of practice (36%; 23%), absenteeism (23%; 0%), sinonasal (66%; 20%) and gastroesophageal symptoms (44%; 22%), hoarseness (82%; 78%), throat clearing (70%; 62%), and phonatory effort (72%; 52%). In both groups, there were decreased values of maximum phonation time, impairment of the G parameter in the GRBASI scale (82%), decrease of F0 and increase of the rest of acoustic parameters. Nodules and laryngopharyngeal reflux were predominant in teachers; laryngopharyngeal reflux, polyps, and sulcus vocalis predominated in the controls. Vocal symptoms, comorbidities, and absenteeism were predominant among teachers. The vocal analyses were similar in both groups. Nodules and laryngopharyngeal reflux were predominant among teachers, whereas polyps, laryngopharyngeal reflux, and sulcus were predominant among controls.

Números Complexos: um estudo histórico sobre sua abordagem na coleção Matemática 2º ciclo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)